A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence of a unique stationary density and give sufficient conditions for asymptotic stability.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-2-2,
author = {Michael C. Mackey and Marta Tyran-Kami\'nska},
title = {Dynamics and density evolution in piecewise deterministic growth processes},
journal = {Annales Polonici Mathematici},
volume = {93},
year = {2008},
pages = {111-129},
zbl = {1183.47038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-2-2}
}
Michael C. Mackey; Marta Tyran-Kamińska. Dynamics and density evolution in piecewise deterministic growth processes. Annales Polonici Mathematici, Tome 93 (2008) pp. 111-129. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-2-2/